Problem: Divide the polynomials.
Explanation: Usually, there are many different ways to divide polynomials. Here, we will use the method of factoring and canceling common factors. Try to factor the numerator, and see if you end up with a common factor to cancel with the denominator. Factoring the numerator $4x^3+x^2=x(4x^2+x)$ Canceling common factors $\begin{aligned} \dfrac{4x^3+x^2}{x}&=\dfrac{\cancel{x}(4x^2+x)}{\cancel{x}} \\\\ &=4x^2+x \end{aligned}$ In conclusion, this is the result of dividing the polynomials: $4x^2+x$ [I want to see a different way of performing the division.]